A statement that appears to be true but has not yet been proved is a ______.
- counterexample
- guess
- conjecture
- proof
A statement that appears to be true but has not yet been proved is a conjecture.
A statement that appears to be true but has not yet been proved is a conjecture.
A statement that appears to be true but has not yet been proved is a conjecture.
A statement that appears to be true but has not yet been proved is a conjecture.
An example showing that a conjecture is not true is called a _____.
- false statement
- proof
- formal proof
- counterexample
An example showing that a conjecture is not true is called a counterexample.
An example showing that a conjecture is not true is called a counterexample.
An example showing that a conjecture is not true is called a counterexample.
An example showing that a conjecture is not true is called a counterexample.
Showing some specific examples that are true for a conjecture shows that it is always true.
- true
- false
Specific examples may show that a conjecture is true some of the time, but a formal proof is necessary to prove a conjecture is always true.
Specific examples may show that a conjecture is true some of the time, but a formal proof is necessary to prove a conjecture is always true.
Which of the following would prove that the given conjecture is always true?
Conjecture: The sum of two consecutive integers is an odd number.
- First number = x, second number = x + 1.
Sum = (x) + (x + 1) = 2x + 1 - First number = 10, second number = 11.
Sum = (10) + (11) = 21 - First number = 100, second number = 200.
Sum = (100) + (200) = 300 - This is not a true conjecture.
Sum = (x) + (x + 1) = 2x + 1 proves the conjecture by taking any two consecutive numbers into account.
Sum = (x) + (x + 1) = 2x + 1 proves the conjecture by taking any two consecutive numbers into account.
Sum = (x) + (x + 1) = 2x + 1 proves the conjecture by taking any two consecutive numbers into account.
Sum = (x) + (x + 1) = 2x + 1 proves the conjecture by taking any two consecutive numbers into account.
Summary
Questions answered correctly:
Questions answered incorrectly:
